Problem: Determine the intercepts of the line. $ 9x-7y=14$ $x$ -intercept: $\Big($
Solution: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}9x-7\cdot{0}&=14\\ 9x&=14\\ x&=\dfrac{14}{9}\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{14}{9},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}9\cdot{0}-7y&=14\\ -7y&=14\\ y&=-2\end{aligned}$ So the $y$ -intercept is $\left(0,-2\right)$. In conclusion, The $x$ -intercept is $\left(\dfrac{14}{9},0\right)$. The $y$ -intercept is $\left(0,-2\right)$.